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When water is heated but not yet boiling, I understand that the intermolecular attraction does not change, but the molecules vibrate more.

But when water boils to gas, does the forces of attraction between the molecules change, or are the intermolecular forces simply broken?

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Intermolecular forces are never broken. What can be broken are bonds, although one should add that the precise concept of a bond is not straightforward (there are no hooks joining molecules).

From a fundamental point of view, all the interactions relevant in typical condensed matter systems are basically electrostatic. Different kinds of bonds (covalent, ionic, metallic, van der Waals, etc.) are just other names given to extreme cases. They continuously modify one into another as a function of distances and environmental conditions. An accurate solution to the electronic problem of a set of Hydrogen and Oxygen atoms for each nuclear position would be enough to provide a good description of the molecular interactions within the so-called Born-Oppenheimer approximation.

People still use classical model potential for many reasons, including the computational cost of accurate ab-Initio calculations. There are many of them available for water. I just cite TIP4P/2005 or SPC/E as a couple of popular choices good enough to be used for many computer simulations of different properties of water and aqueous systems. At the level of such model potential, it may be necessary to modify them as a function of the thermodynamic phase (although it is not always the case). However, it should be clear that this is just an effect of an approximate description of the interactions. It is not a conceptual necessity.

The problem of accurately determining the liquid-vapor coexistence properties may require some expressly modified adaption, as seen in a recent paper on this issue.

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Interactions between molecules of water are always the same, regardless of the temperature and the phase. What happens when you heat water is that the increase in temperature causes the water molecules to have higher average velocity, so they can overcome the attractive interactions and a gas forms.

The reason why this happens discontinuously, in a first-order phase transition, is actually quite complicated, but intutively what happens is that the liquid state (of high density) becomes more energetically unfavourable than gaseous one (of low density). As a consequence, all the system "jumps" at once to the gaseous state and a sudden change in water's properties happens. That is what makes boiling water different from heated water. Notice that no change in the interactive forces was involved in this sudden change.

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